def test_sparse_regression():
"""
Test sparse regression
"""
A, y, x_true = generate_sparse_system()
# least squares solution
xls = np.linalg.lstsq(A, y)[0]
# proximal algorithm for sparse regression
opt = ADMM(xls)
opt.add('linsys', A=A, b=y)
opt.add('sparse', 1.)
opt.display = None
opt.storage = None
opt.run(maxiter=100)
xhat = opt.theta
test_err = np.linalg.norm(xhat - x_true, 2)
naive_err = np.linalg.norm(xls - x_true, 2)
err_ratio = test_err / naive_err
print("The error ratio is: %5.4f" % err_ratio)
assert err_ratio <= 0.01
def test_lowrank_matrix_approx():
"""
Test low rank matrix approximation
"""
Xobs, Xtrue = generate_lowrank_matrix()
# proximal algorithm for low rank matrix approximation
opt = ADMM(Xobs)
opt.add('squared_error', Xobs)
opt.add('nucnorm', 0.2)
opt.display = None
opt.storage = None
opt.run(maxiter=100)
Xhat = opt.theta
test_err = np.linalg.norm(Xhat - Xtrue, 'fro')
naive_err = np.linalg.norm(Xobs - Xtrue, 'fro')
err_ratio = test_err / naive_err
print("The error ratio is: %5.4f" % err_ratio)
assert err_ratio <= 0.5
